New method for clear day selection based on normalized least mean square algorithm

Abstract

A new method is proposed to select clear days from data sets of solar irradiation recorded with ground-based instruments. The knowledge of clear days for a given site is of prime importance both for the study of turbidity and for the validation of empirical models of global solar radiation (GSR). Our innovative method is based on the normalized least mean square (NLMS) algorithm that estimates noise according to a GSR model. The developed method named clear day selection method (CDSM) is compared with the well-known clearness index criteria (kt) taking data collected at Tamanrasset in Algeria during the period 2005–2009. The root mean square error (rmse), the mean absolute percentage error (mape), and the dependence of model error (mbe) are considered for the comparison. A different number of clear days is found with both methods, with additionally a kt dependency for the clearness index criteria. The average values of rmse, mape, and mbe between the daily average of the measured GSR and its estimate using a model are better in the case of CDSM for the period 2005–2009. Indeed, we found 25.28 W/m2, 4.61%, and 2.09 W/m2 respectively for CDSM and 42.48 W/m2, 7.63%, and − 5.91 W/m2 for the clearness index method with kt = 0.7. We also found that GSR of clear days is well correlated with the model in the case of CDSM, which gives good confidence in our results.